Differential cross sections for electromagnetic fission of U-238 projectiles (500 MeV/u) in C, Sn, and Pb targets are measured and analyzed in terms of single- and multiphonon giant resonance excitations as doorway states to fission. A novel experimental method exploits the linear relationship between neutron multiplicity and the primary U-238 excitation energy. Multiphonon states contribute up to 20% of the cross section; a component at high excitation energies is indicated that may arise from three-phonon dipole and two-phonon GDRxGQR(iv) giant resonance excitations.